1324482 九、發明說明： 【發明所屬之技術領域】 本發明是有關於一種視訊編碼之演算法，且特別是有 關於一種採用搜尋固定間隔之候選基準點，以減少取樣的 數目，並搭配小範圍全區域搜尋法之視訊編碼演算法》 【先前技術】 H.264/AVC是國際電信聯盟遠程通信標卑化組（ITU-T) 内的視訊編碼專家組（Video Coding Experts Group ; VCEG) 與國際標準組織（ISO)/國際電工協會（IEC)下的動態圖像專 家組（Moving Picture Experts Group ; MPEG)共同組成的聯 合視訊組（Joint Video Team ; JVT)所制訂的視訊壓縮標準。 此視訊壓縮標準的主要目標為高效能，具有網路親和 性（network friendly)及具備抗誤性（error resilience)。相較 於習知的14?£0-1，1\^£0-2，^«^0-4，與11.263++等視 訊編碼方式，H.264/AVC視訊壓縮標準提出更多樣的判別 模式種類，且複雜度更高的混合式區塊表示法（Variable Block Sizes)，以及多張參考畫面（Multiple Reference Frame ; MRF)之搜尋法。 由於上述的技術，導致在習知編碼系統中已經佔去龐 大計算量的位移預測（Motion Estimation)部分，將增加更多 的計算量。因此，為了達到高晝質電視（High Definition Television; HDTV)應用與即時編碼之目標，如何在龐大的 計算量下提升整體效能與總體輸出率是一項必須要克服 5 的議題。 在編碼程序中’頁框間預測（Inter-Frame prejiction) ;讀度決疋了母個晝面品質的好壞。而分數點位移的預 測疋根據整數點位移預測的結果再進一步搜尋。因此，精 T的整數點預測，才能使得整體的畫面品質不會失真。在 ^的4實作上’絕大部分都採用全區域搜尋演算法做 ^硬體實作的内容。-方面不會有整數點位移預測的失 =另4面則因為規律性的搜尋方式，可以大量重複利 目同的貝料’以減少頻繁的記憶體存取動作。不過這個 ^有的缺點，就是耗費極大的硬體成本，並極為 於面積曰益縮減的晶片中。衷算去實在不適合實作 因此，減少大量的記憶體存取動作 頻寬需求，均為習4杜& 降低汁算所南之 均為％知技術亟待克服的問題。 【發明内容】 為解決上述和其他的問題， 技術優點，本發明提供_種適達到本發明所主張的 法D '、視訊編碼標準之演算 因此本發明的目的就是 移預測演算法，用以減少編碼程序中—段式之整數位 所需時間。 &理每一區塊搜尋的 本發明的另一目的是在提供— 之視訊編碼方法，用以選 、種預測最佳位移向量 〜擇所需位元數最少，準確性佳之 1324482 位移向量。 根據本發明之上述目的，提出一種兩階段之整數位移 預測演算法《依照本發明一較佳實施例，在第一階段中， 每間隔一個固定的取樣點進行一次搜尋，藉此規律性的搜 尋動作，可大量節省因同樣的資料需求所耗費的記憶體存 取時間；決定數個候選基準點（Candidate)後，尚能快速地 獲得數個接近最佳解的位移向量（Motion Vector)。第二階 • 段，針對第一階段決定的數個候選基準點，進行小範圍全 區域搜尋（Local Small Range Full Search)。由於第一階段 中已獲得接近最佳解的位移向量，所以需針對這些位移向 量的趨勢做更進一步的搜尋；依據所搜尋的所有區塊，找 出最佳的4x4區塊位移預測。最後從剩下的區塊種類 (Block Modes)中，選出各種區塊種類中最佳的41筆位移 向量，再輸出至分數位移預測（Fractional Motion Estimation ; FME)執行更準確的預測。 • 根據本發明之目的，提出一種預測最佳位移向量之視 訊編碼方法。依照本發明一較佳實施例，由預測向量 (Prediction Vector)預測每個區塊被編碼之後的位元數，以 及拉格朗治型模式決定方式（Lagrangian Mode Decision Method)運算出來的初始權重（Initial Weight)模式；接著因 應每個區塊的不同組合’配合其權重，藉以選擇編碼之後 用到的位元數最少，但不失其準確性的最佳位移向量。 根據上述内容，本發明具有下列優點： 1.本發明採用固定間隔的搜尋方式，可以避免當晝面 7 内容位移很大時， 真狀況。 習知之固定位置搜尋法所可能產生的失 針對夕張參考畫面搜尋，本發明可以在每張搜尋 面都只做第-階段的循序跳點搜尋，而第二階段 ^ 一階段㈣讀錢縣相，並進—倾料可得5 取佳⑽向量Q藉此方法可較習知技術大幅節劣運算量。 【實施方式】 參照第1圖，其繪示依照本發明一較佳實施例的—種 整數位移預測（lntegral M〇ti〇n Estimati⑽；！ME)演算法之 不思圖。本發明提出了二階段式的整數位移預測演算法， 在第一階段110,進行規律性的搜尋，取得數個在搜尋>範 圍’即第1圖中的像素位於·16到15位置，内出現的較佳 位移區塊；再於第二㈣120找出真正位於這些較佳位移 區塊呈現的趨勢中包含的最佳位移向量。 第一階段110中，每間隔一個固定的取樣點進行一次 搜尋，藉此規律性的搜尋動作，可大量節省因同樣的資料 而求所耗費的存取時間；決定數個候選基準點（Candidate) 後，才能快速地獲得數個接近最佳解的位移向量（Motion Vector)。 另外，在第一階段110中進行運算時，由於無需決定 最後之位移向量，因此運算時不需達到全字元精確度，只 需擷取畫素中之數個高位元，即可減少記憶體存取之頻寬 需求。此外，為配合實作混合式區塊表示（Variable Bl〇ck 1^^44821324482 IX. Description of the Invention: [Technical Field] The present invention relates to a video coding algorithm, and in particular to a candidate reference point using a search fixed interval to reduce the number of samples, and with a small range Video Coding Algorithm for Region-wide Search Method [Prior Art] H.264/AVC is the Video Coding Experts Group (VCEG) and International in the ITU-T International Telecommunications Standards Group (ITU-T). The video compression standard developed by the Joint Video Team (JVT), which is formed by the Moving Picture Experts Group (MPEG) under the Standards Organization (ISO)/International Electrotechnical Commission (IEC). The main goal of this video compression standard is high performance, network friendly and error resilience. Compared with the conventional video encoding methods such as 14? £0-1, 1\^£0-2, ^«^0-4, and 11.263++, the H.264/AVC video compression standard proposes more samples. Discriminating the types of modes, and the more complex Mixed Block Sizes, and the multiple reference frame (MRF) search method. Due to the above techniques, the Motion Estimation portion, which already accounts for a large amount of computation in the conventional coding system, will add more computational complexity. Therefore, in order to achieve the goal of High Definition Television (HDTV) applications and real-time encoding, how to improve the overall performance and overall output rate under a large amount of calculation is an issue that must be overcome. In the encoding program, Inter-Frame prejiction; the reading degree determines the quality of the mother's face. The prediction of the fractional point displacement is further searched based on the results of the integer point displacement prediction. Therefore, the integer point prediction of the fine T can make the overall picture quality not be distorted. In the 4 implementations of ^, most of them use the full-region search algorithm to do the hardware implementation. - There is no loss of integer point displacement prediction = the other 4 sides can be used to reduce the frequent memory access movements because of the regular search method. However, this has the disadvantage of costly hardware costs and is extremely high in wafers with reduced area benefits. In fact, it is not suitable for implementation. Therefore, reducing the bandwidth requirement of a large number of memory access operations is a problem that needs to be overcome by Xi 4 & SUMMARY OF THE INVENTION In order to solve the above and other problems and technical advantages, the present invention provides a method for achieving the calculation of the method D' and the video coding standard claimed by the present invention. Therefore, the object of the present invention is to shift the prediction algorithm to reduce The time required for the integer bit of the segment in the encoding program. Another object of the present invention is to provide a video encoding method for selecting and predicting the optimal displacement vector, selecting the least number of bits required, and performing the 1324482 displacement vector with good accuracy. According to the above object of the present invention, a two-stage integer displacement prediction algorithm is proposed. According to a preferred embodiment of the present invention, in a first stage, a search is performed every fixed sampling point, thereby performing a regular search. Actions can save a lot of memory access time due to the same data requirements; after determining a number of candidate datum points (Candidate), it is possible to quickly obtain several motion vectors close to the optimal solution (Motion Vector). The second-order • segment performs a Local Small Range Full Search for several candidate reference points determined in the first phase. Since the displacement vectors close to the optimal solution have been obtained in the first stage, it is necessary to further search for the trend of these displacement vectors; and to find the best 4x4 block displacement prediction based on all the blocks searched. Finally, from the remaining Block Modes, the best 41 displacement vectors of various block types are selected, and then output to Fractional Motion Estimation (FME) for more accurate prediction. • According to the purpose of the present invention, a video encoding method for predicting an optimal displacement vector is proposed. According to a preferred embodiment of the present invention, the number of bits after each block is encoded is predicted by a Prediction Vector, and the initial weights calculated by the Lagrangian Mode Decision Method ( Initial Weight mode; then, in response to the different combinations of each block, the weights are used to select the best displacement vector with the least number of bits used after encoding, but without losing its accuracy. According to the above, the present invention has the following advantages: 1. The present invention adopts a fixed interval search mode, which can avoid the true situation when the content of the face 7 is greatly displaced. According to the conventional fixed-position search method, the search may be performed on the search screen, and the present invention can only perform the first-stage sequential jump search on each search surface, and the second stage ^ one stage (four) read Qianxian phase, Parallel-pitching can get 5 better (10) vector Q. This method can greatly reduce the computational complexity compared with the prior art. [Embodiment] Referring to Figure 1, there is shown an idea of an integer displacement prediction (lntegral M〇ti〇n Estimati(10);!ME) algorithm in accordance with a preferred embodiment of the present invention. The present invention proposes a two-stage integer displacement prediction algorithm. In the first stage 110, a regular search is performed to obtain a plurality of pixels in the search > range, that is, the pixels in the first picture are located at positions 16 to 15, The preferred displacement block appears; and the second (four) 120 finds the best displacement vector that is actually included in the trend presented by the preferred displacement blocks. In the first stage 110, a search is performed every time a fixed sampling point is used, thereby regularly searching for a large amount of access time for the same data; determining a number of candidate reference points (Candidate) After that, you can quickly get several motion vectors close to the optimal solution (Motion Vector). In addition, when the operation is performed in the first stage 110, since it is not necessary to determine the final displacement vector, the full character accuracy is not required to be calculated, and only a few high bits in the pixel can be extracted to reduce the memory. The bandwidth requirement for access. In addition, in order to cooperate with the implementation of mixed block representation (Variable Bl〇ck 1^^4482
Sizes)之位移向量搜尋，本階段僅須計算單一大小之區塊 即可，如16χ16巨集區塊模式之運算，以上兩種實施方法 均可大幅節省運算量，並維持位移向量之精確度。 第一階段120，係針對第一階段u〇所決定的數個候 選基準點，進行小範圍全區域搜尋（Local Small Range Full Search)。由於在第一階段11〇已獲得數個接近最佳解的候 選基準點，所以需針對這些位移向量的趨勢做更進一步的 搜尋；從候選基準點開始，周圍做小範圍的全區域搜尋， 再依據所搜尋的所有向量，找出最佳的4χ4區塊位移預 測最後從剩下的區塊種類（Block Modes)中，選出各種區 塊種類中最佳的41組位移向量。 參照第2圖，其繪示依照本發明一較佳實施例的一種 整數位移預測之編碼流程圖。當處理一巨集區塊所包含之 資料時’首先，步驟210係將目前所得到的位移向量，根 據預測向量預測每個區塊編碼之後的位元數，以及配合拉 格朗治型模式決定方式運算出初始權重；步驟22〇係將欲 運算的參考巨集區塊像素（Reference Macr〇bl〇ck Pixel)與 目前巨集區塊像素（Current Macroblock Pixel)加以減少傳 輸資料位元數，以達到減少硬體成本和節省記憶體存取頻 寬的優勢，而步驟230係每隔一個固定的間距搜尋位於搜 尋範圍内的所有位移區塊’一直持續至步驟240的找出目 前畫面（Current Frame)的動態趨勢，即若干個最佳的位移 區塊。至此，第一階段110的運算已處理完畢。若要處理 多張參考晝面搜尋，則必須循序搜尋前一張晝面、前二張 9 1324482 畫面類推’直到所欲搜尋的張數為止。 根據第-階段m所找出之候 圍的全域搜尋，並從中獲得最佳的=塊^事小範 120的目禪。由於太| 〇里則是第二階段 的=纟於本發明是從1塊搜㈣ 範圍，找到可能最佳的位移趨勢。在 内縮小 尋每個可能的候選基準點，並採用了步驟26=’依序搜 區域搜尋方式，直到Μ範圍全 止，最後的步驟27〇為根據；；r選基準點都搜尋過為 ，娜ου马根據Η 264解 的41组位移向量，選—組位移:: := 一組16X16巨集區塊模式，兩·…巨集區塊模气： 組8x16巨集區塊模式、一巨集區塊模式!= 塊模式、八組4χ8巨集區塊模式和十六 =模式1❹w㈣㈣行更進—步的運算; 的I::二第1表其列示依照本發明-較佳實施例 的-種權重產生器用以計算權重的預測編碼所產生之位 元數。本發明藉由參考驗證軟體JM(References〇fweSizes) displacement vector search, only need to calculate a single size block at this stage, such as 16 χ 16 macro block mode operation, the above two implementation methods can greatly save the amount of calculation, and maintain the accuracy of the displacement vector. In the first stage 120, a small-area full-area search (Local Small Range Full Search) is performed for a plurality of candidate reference points determined by the first stage. Since a number of candidate reference points close to the optimal solution have been obtained in the first stage, it is necessary to further search for the trend of these displacement vectors; starting from the candidate reference point, a small-area full-area search is performed around, and then According to all the vectors searched, find the best 4χ4 block displacement prediction. Finally, from the remaining Block Modes, select the best 41 sets of displacement vectors of various block types. Referring to Figure 2, there is shown an encoding flow chart for integer displacement prediction in accordance with a preferred embodiment of the present invention. When processing the data contained in a macroblock, 'Firstly, step 210 is to predict the current displacement vector based on the prediction vector, and determine the number of bits after each block encoding, and the Lagrangian mode. The method calculates the initial weight; in step 22, the reference macroblock pixel to be operated (Reference Macr〇bl〇ck Pixel) and the current macroblock pixel (Current Macroblock Pixel) are used to reduce the number of transmission data bits, To achieve the advantage of reducing hardware cost and saving memory access bandwidth, step 230 searches for all the displacement blocks located in the search range every other fixed interval' until the current picture is found in step 240 (Current Frame) Dynamic trend, that is, several optimal displacement blocks. At this point, the operation of the first stage 110 has been processed. To process multiple reference facets, you must search for the previous page and the first two sheets of the 13 1324482 screens until the number of sheets you want to search. According to the global search of the waiting period found in the first stage m, and obtain the best = block ^ Xiaofan 120. Since too | 〇里 is the second stage = 纟 in the present invention is from the range of 1 search (four), find the best possible displacement trend. Zoom out to find each possible candidate reference point, and use step 26 = 'sequential search area search mode until the Μ range is complete, the last step 27 is based;; r select the reference point to search for, According to the 41 sets of displacement vectors solved by Η 264, the selection group displacement:: := A set of 16X16 macro block mode, two... macro block block mode gas: group 8x16 macro block mode, a giant Set block mode! = block mode, eight sets of 4 χ 8 macro block mode and sixteen = mode 1 ❹ w (four) (four) line further step-by-step operation; I:: two first table which is listed in accordance with the present invention - preferred embodiment The weight generator is used to calculate the number of bits generated by the predictive coding of the weight. The invention uses the reference verification software JM (References〇fwe
Joint M〇del)9.3研發了 一套預測方式，此方式可預測目前 的位移向量將會被編竭成如第1表中所示之位元數，第一 表中的搜尋範圍為10表示搜尋像素範圍在㈠6，+】6)。並運 用此預測數據’加上預設位移向量以及Η ·標準編碼程 序所提出的拉格朗治型模式決定方式，共同運算出所需的 初始權重。 1324482 第1表 搜尋範!圍=16 (Search Range = 16) 範圍（Range) 位元數（Bit Number) 0 1 1 3 2~3 5 4〜7 7 8~15 9 16 〜31 11 32 〜63 13 64 〜127 15 128 〜255 17 256 〜512 19Joint M〇del) 9.3 developed a set of prediction methods that predict that the current displacement vector will be compiled into the number of bits as shown in Table 1. The search range in the first table is 10 for search. The pixel range is (1) 6, +] 6). And using the predicted data 'plus the preset displacement vector and the Lagrangian mode decision method proposed by the standard encoding program, jointly calculate the required initial weight. 1324482 Table 1 search range! Range = 16 (Search Range = 16) Range (Bit Number) 0 1 1 3 2~3 5 4~7 7 8~15 9 16 ~ 31 11 32 ~ 63 13 64 ～127 15 128 ～255 17 256 ～512 19
參照第3圖，其繪示依照本發明一較佳實施例的一種 減少傳輸資料位元數之方式示意圖。本發明直接採用前面 四個位元，稱為最高有效位元（Most Significant Bit ; MSB)3 10，而省略了後面四個位元，稱為最低有效位元 (Least Significant Bit ; LSB)320。 原因為省略掉最低有效位元320時，晝面品質減損甚 微，若超過四個位元，則畫面品質將失真到人眼可察覺的 程度；且若省略了最低有效位元，則後續處理之硬體元件 僅使用四位元加法器330即可，節省了原本需使用八位元 加法器的硬體成本。另外，從晶片外記憶體存取資料時， 更可以將資料存取時間減少為原來的二分之一。 參照第4圖，其繪示依照本發明一較佳實施例的一種 第一階段產生較佳位移向量之流程圖。一邊運算絕對值差 11 1324482 的總和（Sum of Absolute Difference ; SAD)，接著比較尚未 處理之絕對值差的總和41〇,與進入候選基準表中可能性 最高的絕對值差的總和420，兩者之間的大小為何；若前 者小於後者，則將其插入候選基準表中並依可能性的大小 加以排序，可能性越咼的候選位移向量區塊放置在候選基 準點名單的前面；若有更好的位移向量選擇，則馬上更新 緩衝儲存器（Data Buffef)裡时料；若前者不小於後者， 則將該筆資料丟棄’不進行計算。當整個區域搜尋完之 後’即可得到目前晝面的趨勢(即完成帛2圖中的 240) 〇 由上述本發明較佳實施例可知，應用本發明具有下列Referring to FIG. 3, a schematic diagram of a method for reducing the number of transmitted data bits according to a preferred embodiment of the present invention is shown. The present invention directly uses the first four bits, called the Most Significant Bit (MSB) 3 10, and omits the last four bits, called the Least Significant Bit (LSB) 320. The reason is that when the least significant bit 320 is omitted, the quality of the facet is slightly degraded. If it exceeds four bits, the picture quality will be distorted to the extent that the human eye can perceive; and if the least significant bit is omitted, the subsequent processing The hardware component only uses the four-bit adder 330, which saves the hardware cost of using the octet adder. In addition, when accessing data from off-chip memory, the data access time can be reduced to one-half. Referring to Figure 4, there is shown a flow chart for generating a preferred displacement vector for the first stage in accordance with a preferred embodiment of the present invention. Calculating the sum of the absolute value difference 11 1324482 (Sum of Absolute Difference; SAD), and then comparing the sum of the absolute value differences that have not been processed 41〇, and the sum 420 of the most likely absolute value differences into the candidate reference table, both If the former is smaller than the latter, it is inserted into the candidate reference table and sorted according to the size of the possibility. The candidate vector block with the possibility of being more ambiguous is placed in front of the candidate reference list; if there is more If a good displacement vector is selected, the data in the buffer (Data Buffef) is updated immediately; if the former is not less than the latter, the data is discarded 'no calculation. When the entire area is searched, the trend of the current face is obtained (i.e., 240 in the completed Fig. 2). 〇 According to the preferred embodiment of the present invention described above, the application of the present invention has the following
1.本發明採用在小區域内以固定間隔搜尋所有可能 候選基準點的方式，除了能找出各個候選基準點最佳的位 移向量及其變動趨勢之外，亦能避免當畫面内容的位移很 大時’習知之搜尋法所可能產生的失真狀況。 若需要對多張參考畫面搜尋，本發明可以在每張搜 只做第一階段的循序跳點搜尋，更可以根據不同 整晝質IS體數目的候選基準區塊，來動態的調 位於各* 的需未°而第二階段僅需找出第-階段 ;各=的最佳候選基準點，並進一步搜尋即可得到最 二移^。藉纽整數位移㈣方法，針對每—個搜尋 是搜尋4張參考畫面，第一階段每5點跳 哥選出4個候選基準點，第二階段搜尋位於4個候選基 12 1324482 準點周圍的（-2，+2)像素，則只需要 (((16*2)/5 + 1)λ2*4)+4*((2*2+1)α2) = 296 的搜尋次數；而全 區域搜尋則需要（（16*2+1)八2)*4 = 4356的搜尋次數，可較 習知之全區域搜尋法節省（4356-296)/4356=93%以上的運 算量。 3.因為本發明所採用之演算法包含規律性的搜尋方 式，可以大量重複利用相同的資料，以減少頻繁的記憶體 存取動作，進而大幅降低系統對記憶體之頻寬需求。 雖然本發明已以一較佳實施例揭露如上，然其並非用 以限疋本發明，任何熟習此技藝者，在不脫離本發明之精 神和範圍内，當可作各種之更動與潤飾，因此本發明之保 護範圍當視後附之申請專利範圍所界定者為準。 【圖式簡單說明】 為讓本發明之上述和其他目的、特徵、優點與實施例 能更明顯易懂’所附圖式之詳細說明如下： 第1圖係繪示依照本發明一較佳實施例的—種整數位 移預測（Inte㈣Motion Estimati〇n ; IME)演算法之示意圖。 第2圖係繪示依照本發明一較佳實施例的-種整數位 移預測之編碼流程圖。 第3圖係繪示依照本發明—較佳實施例的_種第—階 段產生較佳位移向量之流程圖。 / 4圖料示依照本發日卜較㈣施例的-種減少傳 輸資料位元數之方式示意圖。 13 1324482 【主要元件符號說明】 110 :第一階段 210 :步驟 230 :步驟 250 :步驟 270 :步驟 320 :最低有效位元 410:尚未處理之絕對值差的 :第二階段 :步驟 :步驟 :步驟 :最南有效位元 :四位元加法器 :可能性最高的絕對值差1. The present invention adopts a method of searching all possible candidate reference points at regular intervals in a small area. In addition to finding the optimal displacement vector of each candidate reference point and its variation trend, it can also avoid the displacement of the screen content. The distortion that may occur in the search method of the big time. If it is necessary to search for a plurality of reference pictures, the present invention can only perform the first stage of the sequential jump point search in each search, and can dynamically adjust the position according to the candidate reference blocks of the number of different whole body IS bodies. The second stage only needs to find the first stage; the best candidate reference point of each = and further search to get the second most. By means of the integer integer displacement (four) method, for each search, 4 reference pictures are searched. In the first stage, 4 candidate reference points are selected for every 5 points, and the second stage search is located around 4 candidate bases 12 1324482. 2, +2) pixels, only need ((16 * 2) / 5 + 1) λ2 * 4) + 4 * ((2 * 2 + 1) α2) = 296 search times; The number of searches for ((16*2+1)8-2)*4=4356 is required, which can save (4356-296)/4356=93% of the calculation amount compared with the conventional full-area search method. 3. Since the algorithm used in the present invention includes a regular search method, the same data can be reused in a large amount to reduce frequent memory access operations, thereby greatly reducing the system's bandwidth requirement for memory. Although the present invention has been described above in terms of a preferred embodiment, it is not intended to limit the invention, and it is obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit and scope of the invention. The scope of the invention is defined by the scope of the appended claims. BRIEF DESCRIPTION OF THE DRAWINGS The above and other objects, features, advantages and embodiments of the present invention will become more <RTIgt; An example of an integer displacement prediction (Inte (4) Motion Estimati〇n; IME) algorithm. Figure 2 is a flow chart showing the encoding of integer bit shift prediction in accordance with a preferred embodiment of the present invention. Figure 3 is a flow chart showing the generation of a preferred displacement vector in accordance with the first stage of the preferred embodiment of the present invention. / 4 The figure shows a schematic diagram of the method of reducing the number of bits of transmission data according to the application of the present invention. 13 1324482 [Description of main component symbols] 110: First stage 210: Step 230: Step 250: Step 270: Step 320: Least significant bit 410: Absolute value difference not yet processed: Second stage: Step: Step: Step : Southernmost significant bit: four-bit adder: the most likely absolute difference